(CNN) -- Mexican authorities are searching for an American boater reported to have been killed by pirates on a lake that straddles the U.S.-Mexico border, but have not yet found his remains, a state police commander said Tuesday.
Rolando Flores, lead investigator for the Tamaulipas state police, told CNN that Mexican troops and sailors are taking part in the search, but described the area as "a conflict zone."
"The zone where it happened is in control of organized criminals," Flores said. "That's their territory. The area is inhabited by them, ranchers and steers."
The wife of the missing man, 30-year-old David Hartley, reported that gunmen in three boats approached them Thursday and shot her husband, who fell off his personal watercraft into Lake Falcon. In a CNN interview Tuesday afternoon, Hartley's mother, Pam Hartley, choked back tears as she pleaded with Mexican authorities to allow American volunteers to join the effort.
"What I hear is that Mexico will not let us go over there," she said. "They don't have the resources to do a thorough search. So if that's the case, please let us cross the border and start searching for him."
Ruben Dario Rios, spokesman for the Tamaulipas attorney general's office, said the operation was still going on. But until the family files an official complaint with Mexican authorities, "everything is being done informally."
Hartley's wife, Tiffany, is expected to file a complaint at the attorney general's office in Miguel Aleman on Wednesday, he told CNN en Espanol.
Lake Falcon is about 200 miles south of San Antonio, Texas, and about 70 miles west of the Hartleys' home in McAllen. Flores said he has been in touch with sheriff's deputies across the border in Zapata County, but said U.S. officials have not yet requested a formal investigation and that investigators had no way of knowing whether the reported incident actually took place.
"We've received the GPS coordinates from the United States of where this alleged incident happened, and we have not located a body," Flores said. But he added, "We understand the magnitude of this case."
Tiffany Hartley reported that she and her husband were riding personal watercraft Thursday on the Mexican side of the lake when they were attacked. Hartley was shot and fell into the water, she told sheriff's deputies in Zapata County, Texas.
"He was thrown off the Jet Ski and I couldn't pick him up to get him on mine," Hartley told a sheriff's dispatcher in a 911 call released by the agency.
Later, she told CNN affiliate KRGV that she saw her husband was shot in the head and also had a gun pointed at her.
"When I was pulling him up, I just kept hearing God say -- you gotta go, you gotta go. And I looked back at the other boats to see where they were. And they were heading back to me," she told KRGV. "So I let David back in the water."
Tamaulipas has made headlines recently as a hotbed for drug cartel violence, and Zapata County Sheriff Sigifredo Gonzalez Jr. said he believes the attackers were pirates linked to the cartels. There have been at least four cases of gunmen in Mexican waters robbing or threatening boaters on Lake Falcon since April, according to the Texas Department of Public Safety.
The department has warned Americans to stay on the U.S. side of the lake since May. But Pam Hartley said her son and daughter-in-law "know where to go and where not to go."
"He never would have taken Tiffany anywhere where she would have been in danger. Never," she said.
The couple's relatives have publicly called on Mexico to step up its efforts to find Hartley, and speaking on the CBS "Early Show" on Tuesday, Tiffany Hartley dismissed suggestions from Mexican authorities that they could not verify the shooting.
"I can understand why they would be asking the questions," she said. But she added, "They haven't been looking, either, as far as we know." She suggested that the still-unidentified killers may still have her husband's body, "and that's why maybe they can't find him."
And Pam Hartley said any suggestion that her daughter-in-law's account was inaccurate is "insane."
"The way Tiffany told it is what happened," Pam Hartley said. "I don't know if they're trying to steer things in a different direction because they don't have to look, or because they don't think it happened. But it did happen, and it happened the way she said it did. And we need to go over there and search for him."
Speaking to KRGV, Tiffany Hartley said she felt awful people might doubt what she said happened to her husband.
"He was my life. He did everything for me. He took care of me. He provided for me. He loved me unconditionally. He was my rock," she told the CNN affiliate, her voice cracking with emotion.
The couple had lived in McAllen and in Mexico for the past three years, said Jenny Mishler, a high-school classmate of both Hartleys. Until about seven months ago, David Hartley had worked for an oil company in the Mexican city of Reynosa, she said, and the Hartleys were planning to move back to northern Colorado -- where they grew up -- this week.
"Their sightseeing trip to Falcon Lake was sort of their last trip there," she said.
Mishler said she and other friends and relatives are planning a rally outside the Mexican Consulate in Denver on Friday in hopes of getting a better response to requests for help from the Mexican government.
"Our whole focus here is to bring them home, or at least to have the Mexican Consulate help us search for him," she said.
The Hartley's congressman, Texas Democrat Henry Cuellar, said he has asked federal agencies to press for support for the search from their Mexican counterparts -- but "so much of it depends on them."
"We want to work with them," Cuellar told CNN en Espanol. "If they need help, we can send some agents."
Lesley Lopez, a Cuellar spokeswoman, said the congressman's office had asked the U.S. Customs and Border Protection agents whether a surveillance drone could be used to search for Hartley's remains, but was told that infrared cameras were unlikely to spot anything due to the length of time that has passed.
CNN's Nick Valencia, Dave Alsup and Matt Smith contributed to this report.